In the area of electronic distance measurement, various principles and methods are known. One approach consists in emitting frequency-modulated electromagnetic radiation, such as, for example, light, to the target to be surveyed and subsequently receiving one or more echoes from back-scattering objects, ideally exclusively from the target to be surveyed, it being possible for the target to be surveyed to have both specular—for example retroreflectors—and diffuse back-scattering characteristics. In an interferometer arrangement, a laser light source is used for the distance measurement. The signal received is superposed with a second signal which is derived from the emitted light signal. The resulting beat frequency of the mixed product, the interferogram, is a measure of the distance to the target object.
This type of interferometry is a well known technique for electro-optic distance measurements that excels by a very high measurement accuracy and shot-noise limited sensitivity. A variety of further embodiments exists ranging from incremental interferometers that operate at a fixed wavelength, to absolute distance meters that may use a multitude of discrete wavelengths (multi-wavelength interferometry), frequency modulated continuous wave interferometry (FMCW) or white-light interferometry.
Absolute distance meters make use of the sensitivity of the interferometric phase φ on the wavelength λ. In the embodiment which is simplest in principle, the optical frequency of the laser source is tuned linearly. As shown below, the distance d—for small wavelength changes—is obtained from
                    d        =                              -                                          λ                2                                            4                ⁢                π                                              ⁢                                    ⅆ              ϕ                                      ⅆ              λ                                                          (        1        )            
The following discussion also applies to multi-wavelength interferometry, where the phase-differences at several wavelengths are measured simultaneously. For the case of two discrete wavelengths λ1, λ2, in equation (1) it can be substituted as follows dλ=λ2−λ1, dφ=φ2−φ1, λ=√{square root over (λ1·λ2)}.
When this technique is applied to non-cooperative targets, well-known effects, so called speckles, emerge that cause a deterioration of measurement accuracy. They appear as stochastic measurement fluctuations that are given by the depth variations within the measurement area, i.e. due to target roughness and target tilt with respect to the measurement beam. These effects are due to randomization of the interferometric phase φ caused by speckles that result from the coherency of the laser-light, which—according to equation (1)—causes a measurement error. The effect occurs to lesser extent with electro-optic distance measurement techniques that use incoherent light—such as classical phase-meter or TOF technologies—where speckle averaging acts to reduce the observed distance variations. Unfortunately, these incoherent techniques have other disadvantages—such as limited measurement accuracy or limited measurement sensitivity—which prevent the replacement of the interferometric techniques.
In prior art a lot of work has been devoted to the problem of randomization of the amplitude, since it may lead to missing detection situations due to destructive interference. In fact, it was shown in W. Goodman, “Some fundamental properties of speckle,” J. Opt. Soc. Am, Vol. 66, No. 11, 1976, p. 1145ff, that the intensity I at each detector location follows an exponential distribution with density function
                              p          ⁡                      (            I            )                          =                              1                          〈              I              〉                                ⁢                      exp            ⁡                          (                                                -                  I                                /                                  〈                  I                  〉                                            )                                                          (        2        )            and therefore, the probability density of the interferometric amplitude A∝√{square root over (I)} follows a Rayleigh-type distribution p(A)=p(I(A))·dI/dA
                              p          ⁡                      (            A            )                          =                                            2              ⁢              A                                      〈                              A                2                            〉                                ⁢                      exp            (                          -                                                A                  2                                                  〈                                      A                    2                                    〉                                                      )                                              (        3        )            
Consequently, the probability of detecting insufficient light to perform a measurement can be high. The methods used to mitigate the effect of these amplitude fluctuations are based on the measurement of decorrelated speckle patterns—a method often termed speckle diversity.
However, the problem of phase randomization has not attracted as much work as the problem of the amplitude variations. For the context of multi-wavelength interferometry in U. Vry and A. F. Fercher, “Higher-order statistical properties of speckle fields and their application to rough-surface interferometry,” J. Opt. Soc. Am. A 3 (1986), p. 988ff a decorrelation of the optical phase with a change of wavelength is revealed which—since the phase is related to distance—leads to distance fluctuations.
According to Y. Salvadé, “Distance Measurement by Multiple Wavelength Interferometry,” Thesis, University of Neuchâtel, 1999, the normalized correlation coefficient of the speckle field at two wavelengths λ1, λ2 corresponding to the synthetic wavelength Λ=λ1·λ2/(λ1−λ2) for an imaging configuration as illustrated in FIG. 1 is given by
                              μ          ⁡                      (            x            )                          =                                            C              p                        ⁡                          [                                                λ                                      M                    ⁢                                                                                  ⁢                    Λ                                                  ⁢                                  (                                      x                    -                                          2                      ⁢                                                                                          ⁢                                              d                        I                                            ⁢                      tan                      ⁢                                                                                          ⁢                      α                                                        )                                            ]                                ⁢                                    exp              ⁡                              [                                                                            2                      ⁢                                                                                          ⁢                      π                      ⁢                                                                                          ⁢                      ⅈ                                        Λ                                    ⁢                                      d                    ⁡                                          (                      x                      )                                                                      ]                                      ·                          exp              ⁡                              (                                                                            -                                                                                          ⁢                                                                        4                          ⁢                                                                                                          ⁢                                                      π                            2                                                                                                    Λ                          2                                                                                      ·                    2                                    ⁢                                                                          ⁢                                      σ                    h                    2                                                  )                                                                        (        4        )            where σh is the target roughness, α the target tilt angle relative to the optical axis, Cp the normalized autocorrelation of the pupil function, dI the distance from the lens to the image plane, M the magnification of the imaging optics, d(x) contains the systematic distance/height profile of the target:
                              d          ⁡                      (            x            )                          =                              2            ⁢                                                  ⁢                          d              0                                +                      d            I                    -                      2            ⁢                                                  ⁢            tan            ⁢                                                  ⁢                          α              ·                              x                M                                              +                                                                                        x                                                  2                                            2                ⁢                                                                  ⁢                                  d                  I                                                      ⁢                          (                              1                +                                  1                  M                                            )                                                          (        5        )            
The variance of the interferometric phase difference between measurements at the two wavelengths is then given by
                              σ          ϕ          2                =                                            π              2                        3                    -                      π            ⁢                                                  ⁢            arcsin            ⁢                                                  ⁢                                        μ                                              +                      arc            ⁢                                                  ⁢                          sin              2                        ⁢                                        μ                                              -                                    1              2                        ⁢                                          ∑                                  n                  =                  1                                ∞                            ⁢                                                μ                                      2                    ⁢                    n                                                                    n                  2                                                                                        (        6        )            
According to (1), this causes stochastic range fluctuations when measuring on rough, tilted targets. Indeed, the standard uncertainty of the measured distance can be roughly estimated by
                              σ          z                ≈                                            δ              ⁢                                                          ⁢              x                        2                    ⁢          tan          ⁢                                          ⁢          α                                    (        7        )            where δx and α are the resolution of the imaging system and the tilt angle, respectively.
In U.S. Pat. No. 5,811,826 a method and an apparatus for remotely sensing the orientation of a plane surface from measuring the speckle pattern of a coherent light beam reflected off the surface are disclosed. The surface is illuminated with radiation of two different frequencies and the corresponding speckle patterns are compared to determine the magnitude and direction of shift from the first speckle pattern to the second. Magnitude and direction of the speckle pattern shift indicates the orientation of the object, i.e. the method measures the lateral shift of the speckle pattern when changing the optical frequency from a first frequency f1 to a second frequency f2 in order to calculate the angle of incidence and the azimuthal angle of the surface.
Although this approach allows a determination of surface properties, like its orientation, the method is based on the use of two different wavelengths at different times whose spectral characteristics have to lead to a sufficient lateral shift of the pattern.